Examining the Error of Mis-Specifying Nonlinear Confounding Effect With Application on Accelerometer-Measured Physical Activity.

PURPOSE: Some confounders are nonlinearly associated with dependent variables, but they are often adjusted using a linear term. The purpose of this study was to examine the error of mis-specifying the nonlinear confounding effect.

METHODS: We carried out a simulation study to investigate the effect of adjusting for a nonlinear confounder in the estimation of a causal relationship between the exposure and outcome in 3 ways: using a linear term, binning into 5 equal-size categories, or using a restricted cubic spline of the confounder. Continuous, binary, and survival outcomes were simulated. We examined the confounder across varying measurement error. In addition, we performed a real data analysis examining the 3 strategies to handle the nonlinear effects of accelerometer-measured physical activity in the National Health and Nutrition Examination Survey 2003-2006 data.

RESULTS: The mis-specification of a nonlinear confounder had little impact on causal effect estimation for continuous outcomes. For binary and survival outcomes, this mis-specification introduced bias, which could be eliminated using spline adjustment only when there is small measurement error of the confounder. Real data analysis showed that the associations between high blood pressure, high cholesterol, and diabetes and mortality adjusted for physical activity with restricted cubic spline were about 3% to 11% larger than their counterparts adjusted with a linear term.

CONCLUSION: For continuous outcomes, confounders with nonlinear effects can be adjusting with a linear term. Spline adjustment should be used for binary and survival outcomes on confounders with small measurement error.